Reservoir models have become an important part of day-to-day decision analysis related to management of oil/gas fields. The concept of ‘closed-loop’ reservoir management is currently receiving considerable attention in the petroleum industry. A ‘real-time’ or ‘continuous’ reservoir model updating technique is an important component for the feasible application of any closed-loop reservoir management process. This technique should be able to rapidly and continuously update reservoir models assimilating the up-to-date measured production data so that the performance predictions and the associated uncertainty are up-to-date for optimization calculations.
The closed-loop reservoir management concept allows real-time decisions to be made that maximize the production potential of a reservoir. These decisions are based on the most current information available about the reservoir model and the associated uncertainty of the information. One important requirement in this real-time, model-based reservoir management process is the ability to rapidly estimate the reservoir models and the associated uncertainty reflecting the most current production data in a real-time fashion.
Traditionally, validation of reservoir models as compared to production data is accomplished through a history matching (HM) process. Conventional history matching methods suffer from one or more of the following drawbacks:                (1) production data for the entire history are matched at the same time and repeated flow simulations of the entire history are required which makes HM extremely time consuming;        (2) gradient based HM methods require sensitivity coefficient calculations and minimization which are complicated, CPU intensive, and often trapped by local minima; and        (3) it is difficult to assess uncertainty with traditional methods and may involve repeating the history matching process with different initial models (this is rarely done because of the time involved to achieve a single history match).        
Thus, despite significant progress made academically and practically, the traditional history matching methods are not well suited for real-time model updating. This is particularly true when a large amount of data are available (e.g., from permanent sensors) and rapid updating of multiple models is required.
The ensemble Kalman filter (EnKF) updating method is well suited for such applications compared to the traditional history matching methods. The unique features of the ensemble Kalman filter are summarized below:                (1) EnKF incrementally updates reservoir models assimilating production data sequentially with time as they become available, thus it is ideally suited for real-time applications;        (2) an ensemble of reservoir models that reflect the most current production data are always maintained. Thus, the performance predictions and uncertainty are always available for optimization study;        (3) EnKF is computationally fast because of the efficiency of parallel/distributing computing;        (4) EnKF can be applied with any reservoir simulator without the need of complicated coding; and        (5) EnKF does not need optimization and sensitivity coefficients calculations.        
These features make EnKF ideal for real-time reservoir model updating. Since its introduction, EnKF has been widely used in Meteorology and Oceanography for data assimilation in large non-linear systems. Evensen, G.: “Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics,” Monthly Weather Review, 127(12), 2741-2758, 1999.
Houtekamer, P. L. and Mitchell, H. L.: “Data assimilation using an ensemble Kalman filter technique,” Monthly Weather Review, 126(3), 796-811, 1998.
Van Leeuwen, P. J. and Evensen, G.: “Data assimilation and inverse methods in terms of probabilities formulation”, Monthly Weather Review 124, 2898-2913, 1996.
Reichle, R. H., McLaughlin, D. B., and Entekhabi, D.: “Hydrologic data assimilation with the ensemble Kalman filter,” Monthly Weather Review, 130(1) 103-114, 2002.
Burgers, G., van Leeuwen, P. J. and Evensen, G.: “Analysis scheme in the ensemble Kalman filter,” Monthly Weather Review, 126, 1719-1724, 1998. Evensen, G.: “The ensemble Kalman filter: Theoretical formulation and practical implementation,” Ocean Dynamics, 53(4), 343-367, 2003.
The ensemble Kalman filter has recently been introduced into the Petroleum industry. Gu, Y. and Oliver, D. S.: “The ensemble Kalman filter for continuous updating of reservoir simulation models,” Computational Geosciences, in press, 2005; Naevdal, G., Mannseth, T., and Vefring, E. H.: “Near-well reservoir monitoring through ensemble Kalman filter,” Paper SPE 75235 presented at the SPE/DOE Improved Oil Recovery Symposium, 13-18 Apr. 2002; and Naevdal, G., Johnsen, L. M., Aanonsen, S. I., and Vefring, E. H.: “Reservoir monitoring and continuous model updating using ensemble Kalman filter”, Paper SPE 84372, presented at the 2003 SPE Annual Technical Conference and Exhibition, Denver, Colo., 5-8 Oct. 2003.
The ensemble Kalman filter can also be used as a history matching technique. Gu, Y. and Oliver, D. S.: “History matching of the PUNQ-S3 reservoir model using the ensemble Kalman filter,” Paper SPE 89942 presented at the 2004 SPE Annual Technical Conference and Exhibition, Houston, Tex., 26-29 Sep. 2004; Liu, N. and Oliver, D. S.: “Critical evaluation of the ensemble Kalman filter on history matching of geological facies,” Paper SPE 92867 presented at the 2005 SPE Reservoir Simulation Symposium, Houston, Tex., 31 January—2 Feb., 2005; Lorentzen, R. J., Naevdal, G., Valles, B., Berg, A. M. and Grimstad, A. A.: “Analysis of the ensemble Kalman filter for estimation of permeability and porosity in reservoir models”, SPE 96375 presented at the 2005 SPE Annual Technical Conference and Exhibition held in Dallas, Tex., 9-12 Oct. 2005; and Tarantola, H.: Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Elsevier, Amsterdam, Netherlands, pp. 613, 1987.
However, current EnKF methodologies have a number of shortcomings. First, conventional EnKF fails to resolve flow equations after Kalman filter updating so that the updated static and dynamic variables may not be consistent, i.e., solutions of the flow equations based on the updated static variables may be different from the updated dynamic variables. Second, the conventional EnKF methods fails to account for nonlinearity and other assumptions made during Kalman updating. Further, conventional EnKF typically require large ensemble sizes to ensure accuracy. The present invention addresses these shortcomings in conventional EnKF methods.